2. Define DOE Factors and Responses for Belt Force Limiter

Why Factor and Response Definition Decides the Whole DOE

In a restraint DOE, the quality of the answer is bounded by the quality of the question. Before any LS-DYNA deck is parameterized, you must commit to three things: which physical knobs you will turn (factors), at what levels you will turn them, and which occupant measurements you will read back (responses). For a belt force limiter study, the natural factor set is the force-limiter load level, the pretensioner firing timing, and the belt routing path. The natural response set is the injury criteria that the restraint system is actually supposed to control: HIC, chest deflection, and femur load. This chapter builds that definition concretely, with a parameter table you can drop into a DOE driver and a response-extraction contract that keeps every run comparable.

Choosing the Three Factors

The belt force limiter is a load-limiting element in the shoulder belt path. Once the pretensioner has removed slack and the occupant loads the belt, the limiter pays out webbing at a controlled force so that the chest is not over-compressed. Three parameters dominate its behavior in a frontal sled model:

• Force limiter load level (FL_LOAD) — the plateau force at which the limiter pays out, typically expressed in kN. This is the single strongest lever on chest deflection and also affects forward excursion and therefore head path.
• Pretensioner timing (PT_TIME) — the time at which the pretensioner pyrotechnic is triggered, in ms from the sled pulse start. Early firing removes slack before the occupant loads the belt; late firing can leave slack that the limiter then has to absorb.
• Belt routing (ROUTE) — a categorical factor describing the belt path over the shoulder and pelvis, for example a nominal routing versus a routing that adds a D-ring offset or a different lap-belt anchor path. Routing changes the belt-to-body angle and therefore the load distribution between chest and pelvis.

These three are chosen because they are physically independent, each is a real design variable in a restraint program, and together they span the trade-off between chest loading and occupant excursion. A DOE that varies only the limiter load will miss the interaction between timing and routing that often dominates real restraint behavior.

Defining Levels and the Factor Matrix

For a screening-style study, three levels per continuous factor and two levels for the categorical routing factor give a manageable but informative design. The table below is the factor definition you would hand to the DOE driver; the level values are teaching example values, not measured data.

With 3 × 3 × 2 = 18 unique combinations, a full factorial is feasible for a single-occupant frontal model and gives clean main effects and two-factor interactions. If run time forces a reduction, a fractional design can be used, but the factor definition itself does not change — only the subset of rows executed.

Defining the Responses

Responses must be extracted the same way in every run, or the DOE compares apples to oranges. Define each response as a named scalar with an explicit extraction rule, a sign convention, and a pass criterion. The three occupant injury responses for this study are:

• HIC15 — head injury criterion computed over the 15 ms window from the resultant head acceleration of the dummy head CG. Report the maximum over the event. Lower is better; a typical design target is below 700 for a frontal occupant.
• Chest deflection (CHEST_DEF) — peak chest compression from the chest deflection transducer, in mm. Report the maximum absolute value. Lower is better; a common target is below 50 mm for a 50th-percentile male.
• Femur load (FEMUR_F) — peak axial compressive force in each femur load cell, in kN. Report the maximum of the left and right femur. Lower is better; a typical target is below 10 kN per femur.

Each response is a scalar so that the DOE post-processor can build a response surface. The extraction rule must specify the signal, the window, and the reduction (max, min, or absolute max). For HIC15 the window is fixed by the criterion; for chest deflection and femur load the window is the full event, typically 0 to 120 ms from sled pulse start.

Parameterizing the LS-DYNA Deck

The factor values must map to concrete LS-DYNA entities. A practical approach is to drive the deck from a small parameter include file and let the DOE driver rewrite it per run. The following snippet shows the mapping contract; the entity names are illustrative and should be matched to your baseline model from the previous chapter.

*PARAMETER
$#   name        value
     FL_LOAD      4.0
     PT_TIME      14.0
     ROUTE_ID     1
$ Belt force limiter: *MAT_ ... or *ELEMENT_SEATBELT_RETRACTOR pay-out force
$ Pretensioner: *INITIAL_... trigger time in ms
$ Routing: *ELEMENT_SEATBELT_PATH / *SET_SEATBELT routing set ID

The DOE driver writes FL_LOAD, PT_TIME, and ROUTE_ID into the parameter block, then launches the solver. The routing factor is categorical, so ROUTE_ID selects between two pre-built belt path definitions rather than scaling a continuous value. This keeps the categorical factor honest: routing is a topology choice, not a number to interpolate.

Response Extraction Contract

After each run, the post-processor reads the dummy output and writes one row per run. The contract below is the minimum needed for a defensible DOE table.

The dashes are placeholders for values produced by the actual runs; they are not measured results and must be filled only after the solver has completed. The table structure is the deliverable: it fixes the factor columns, the response columns, and the run identity so that every downstream analysis is traceable.

How the Factors and Responses Interact

The SVG below shows the causal chain from the three factors through the belt and occupant to the three responses. It is the mental model you should hold while setting up the DOE: the limiter load and pretensioner timing act on the belt force history, routing acts on the belt-to-body geometry, and all three converge on the occupant kinematics that the injury responses measure.

Verification Before Launching the DOE

Before committing 18 runs, verify the parameterization on a single run. Set FL_LOAD = 4.0, PT_TIME = 14, ROUTE_ID = 1, run the model, and confirm three things: the belt force history shows a plateau near 4.0 kN after pretensioner firing, the pretensioner trigger appears at 14 ms in the belt force onset, and the three response values are extracted and written to the run table. If the plateau is absent, the limiter entity is not being driven by the parameter; if the onset is early or late, the timing parameter is mapped to the wrong card; if a response is missing, the extraction rule points at the wrong signal or window. Only after this single-run check passes should the DOE driver be allowed to sweep the factor matrix.

Deliverable: Factor and Response Definition Sheet

The sheet below is the hand-off artifact for this chapter. Fill the response columns only after runs complete; the factor columns and extraction rules are fixed now.

With this sheet fixed, the DOE has a defensible question and a comparable answer for every run. The next step — screening or full factorial execution — can proceed without renegotiating what is being measured.